Abstract

We propose an extension of the Fay-Herriot model to include cases where an underlying distribution in the hierarchical structure may be non-Gaussian. A Gaussian process-based Bayesian technique is developed for this extended framework. We compare the performance of the traditional Gaussianity-based empirical best linear unbiased predictor (EBLUP) and a hierarchical Bayesian prediction technique with the proposed methodology. It is observed that while Bayesian predictors and some frequentist alternatives perform well in some circumstances, the proposed extension fo the Fay-Herriot method is more accurate when Gaussianity is suspect, thus lending robustness to small area studies.